A registered result in its source context

Original ledger classification: E8 vs SO(16) kill tests [E]/[X]: mode D of v347 realised as discriminators -- torus GSD 1 vs 4, level-1 currents 248 vs 120, lattice theta 240 vs 112 norm-2 roots; c=8 alone does NOT decide (v277), only det K=1 (genus-1, v90) selects E8. Falsifiable: a seam with GSD>1 falsifies (E8)_1. SEAM.EQUIV.01 stays [O]

Recorded statement: The empirical/structural DISCRIMINATOR bundle (2026-06-30; mode D of the v347 closure-mode classification) -- concrete FALSIFIABLE kill tests separating the claimed seam=(E8)_1 from the nearest c=8 rival SO(16)_1=(D8)_1. v347 lists four…

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Paper context: Research contracts

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SEAM.E8.DISCRIMINATOR.01

Original claim text

The empirical/structural DISCRIMINATOR bundle (2026-06-30; mode D of the v347 closure-mode classification) -- concrete FALSIFIABLE kill tests separating the claimed seam=(E8)_1 from the nearest c=8 rival SO(16)_1=(D8)_1. v347 lists four closure modes; mode D is 'test the consequences', realised here as sharp discriminators. [E]/[X] PRIMARY/GSD DISCRIMINATOR: |det Cartan(E8)|=1 (ONE primary, holomorphic) vs |det Cartan(D8)=SO(16)|=4 (FOUR primaries 1,v,s,c); torus GSD = #primaries = 1 (E8) vs 4 (SO(16)) -- a seam with GSD>1 / >1 superselection sector falsifies (E8)_1. [E]/[X] CURRENT/THETA DISCRIMINATOR: level-1 current count dim E8=248 vs dim SO(16)=120; the E8 lattice theta has 240 norm-2 roots (=112 integer + 128 spinor, computed) vs D8's 112 -- the affine current spectrum and lattice theta DIFFER; the edge current multiplicity (248 vs 120) is observable. [E] c=8 IS NOT A DISCRIMINATOR: both nets have c=8 (the v277 ambiguity), so the central charge alone cannot decide; only the order-4 mu4 condensation + det K=1 (the genus-1 statement, SEAM.S3.MODULAR.01/v90) selects E8. [E] NON-VACUITY: the discriminators all fire on the rival (det 4!=1, currents 120!=248, roots 112!=240). [X]/[C] VERDICT: the (E8)_1 seam carries sharp falsifiable signatures distinct from every nearby c=8 net (mode D of v347 realised as concrete kill tests); SEAM.EQUIV.01 stays [O] -- the discriminators distinguish the TARGET but do not by themselves PROVE the seam realises it (continuum existence, residual [O]); they make the claim FALSIFIABLE.

Original classification detail

Lattice

Dependencies as recorded

SEAM.EQUIV.01; SEAM.EQUIV.CLOSURE.01; SEAM.S3.MODULAR.01; v347; v90; v89; v281; v422

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Research contracts
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Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
2026-06-30 (six convergent attacks on the one SEAM.EQUIV.01 continuum residual — intrinsic Bisognano–Wichmann, a Lieb–Robinson continuum motor, the [formula in source] -homotopy, an applicability audit, uniform rigidity, and falsifiable kill tests; none closes the keystone, together they reduce it to a single analytic fact and make the claim falsifiable)Research changelog; TFPT — Introduction and reading guide

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Research Contract 1 — [formula in source]tfpt research contracts
Front matter / supportResearch contracts
Research Contract 1 — [formula in source]tfpt research contracts

Registered verification modules

v443_seam_e8_discriminator.pyRegistered verification module · frontier
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SEAM.E8.DISCRIMINATOR.01: the empirical/structural DISCRIMINATOR bundle (mode D of the v347 closure-mode classification) -- concrete FALSIFIABLE kill tests separating the seam=(E8)_1 from the nearest c=8 rival SO(16)_1=(D8)_1. [E]/[X] PRIMARY/GSD: |det Cartan(E8)|=1 (ONE primary, holomorphic) vs |det Cartan(D8)|=4 (FOUR primaries); torus GSD=#primaries=1 vs 4 -- a seam with GSD>1 falsifies (E8)_1. [E]/[X] CURRENT/THETA: level-1 currents dim E8=248 vs dim SO(16)=120; E8 lattice theta has 240 norm-2 roots (=112 integer + 128 spinor, computed) vs D8's 112. [E] c=8 IS NOT A DISCRIMINATOR (the v277 ambiguity); only the order-4 mu4 condensation + det K=1 (genus-1, v90) selects E8. [E] NON-VACUITY: the discriminators all fire on the rival. [X]/[C] mode D as concrete kill tests; SEAM.EQUIV.01 stays [O]. Python-only (dets Wolfram-mirrored via v89/v281/v422).

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